Question

A rectangular sheet of cardbroad is 4 cm by 2 cm. The greatest possible circle is cut off from the cardboard, then the remaining area is

• A. $(16-\pi )c{m}^2$
• B. $(16-4\pi )c{m}^2$
• C. $(8-\pi )c{m}^2$
• D. $(8-4\pi )c{m}^2$

Answer 1

Answer: (C)

$(8-\pi )c{m}^2$

Given,

The dimension of the cardboard $=4cm$ and $2cm$

Area of the cardboard $=4\times 2=8c{m}^2$

Since, the least dimension $=2cm$

The greatest possible circle can have a diameter of maximum $=2cm$

So, the radius of the circle $=1cm$

Area of the circle $=\pi r^2$

$=\pi \times 1^2$

$=\pi c{m}^2$

Therefore, the remaining area will be

$=(8-\pi )c{m}^2$

Hence, this is the answer.